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Introduction to Systems Thinking Concepts

The first session of the workshop offered an introduction to systems thinking concepts with the aims of providing important background to systems thinking approaches and related terminology and exploring specific examples of how systems thinking has been applied in areas of health and medicine, including potential opportunities in the regenerative medicine space. The session was moderated by Claudia Zylberberg of Akron Biotech and featured presentations that described how systems thinking can be applied to the development of regenerative medicines and that explored computational approaches for systems-level data collection.

AN INTRODUCTION TO SYSTEMS THINKING

The speakers in this session discussed how to define systems thinking. The simplest way to define the systems perspective is to contrast it with the reductionist perspective, said William Bialek, the John Archibald Wheeler/Battelle Professor in Physics at Princeton University and the Visiting Presidential Professor of Physics at the Graduate Center of the City University of New York. The reductionist perspective focuses on identifying microscopic components, with the implicit assumption that they can be used to reconstruct macroscopic phenomena. Systems-level thinking focuses on the macroscopic phenomena with a recognition that, while these phenomena ultimately originate from microscopic events, these macroscopic phenomena cannot be easily recreated or predicted using molecular components alone. The dualism between microscopic and macroscopic description distinguishes the two approaches, added Sui Huang, a professor at the Institute for Systems Biology. According to Peter Zandstra, the director of Michael Smith Laboratories and the director and a professor at the School of Biomedical Engineering at The University of British Columbia, conducting work across these scales requires researchers to adapt so that phenomena can be considered in a holistic manner. In his presentation, Bialek went on to provide an overview of systems thinking from his perspective as a theoretical physicist interested in biological problems.

Reductionist Hypotheses Do Not Imply Constructionist Hypotheses

Bialek described the enumeration of the molecular building blocks of life as among the great scientific triumphs of the 20th century. This process of molecular exploration has accelerated into the 21st century due to the ability to look at genome-wide phenomena rather than at single molecules at a time, he said. However, a long-standing problem faced by these efforts is that “the reductionist hypothesis does not imply a ‘constructionist’ one,” in the words of physics Nobel laureate P. W. Anderson in a seminal paper (Anderson, 1972, p. 393). That is, the mere identification

of all building blocks of a system is not tantamount to understanding how to put those pieces back together and to recover the behavior of interest at a macroscopic level. Anderson emphasized conceptual concerns about the relationships among the different sciences, but these issues have practical implications for understanding living systems as well.

Example from Early Fruit Fly Development

To illustrate these implications, Bialek described a biological process that is controlled by a genetic network and considered what can be predicted if all the relevant genes and their interactions have been identified. In the process, many of these genes encode transcription factors that regulate the expression of other genes in the network. A situation in which some genes shape the expression of other genes is not hypothetical, he said, and could describe many biological processes, even in mammalian cells. A classic example of a process controlled by a genetic network is found in early events in the development of a fruit fly, which provided one of the first opportunities to identify all the relevant molecules in a defined biological process. In fruit flies, development occurs along the long axis of the embryo (see Figure 2-1). Female fruit flies generate oocytes (developing eggs) that have crucial molecules serving as developmental landmarks (Alberts et al., 2002). The molecules create morphogen gradients that result in the definition of the anterior, posterior, and other larval structures in the future embryo. The molecules control gene expression, either directly—as transcription factors—or indirectly, as signaling molecules. These molecules are called “gap” genes, as the absence of a gap gene will result in a gap in the body plan of the embryo. These gap genes feed into a set of molecules called “pair-rule” genes, and the striped patterns of pair-rule expression provide a blueprint for the segmented body plan of the fully developed organism. Fruit flies are a particularly useful organism in which to monitor these processes in the laboratory, Bialek said. The transition from maternal effect genes (or maternal inputs) to pair-rule genes occurs in just 3 hours, and after 24 hours the egg hatches and the larva crawls away.

Proliferation of Parameters

All of the molecules involved in this process of fruit fly development have been identified, and the mechanisms represented by arrows in Figure 2-1 have also begun to be understood, Bialek said. However, identifying all the relevant genes and their interactions in a network is not sufficient for developing a model that can make quantitative predictions, due to the proliferation of parameters. For instance, each of the large blue arrows in Figure 2-1 has multiple parameters attached to it. For an arrow that

represents a single transcription factor controlling the expression level of another gene, then the relevant associated parameters include the concentration at which the effect of that control process is half-maximal (i.e., the threshold for “turning things on”) and the sharpness of that threshold. When two or more arrows converge, there is even more hidden complexity, describing how those signals combine; in principle, this could be an arbitrarily complex function. Given that four genes and three inputs are involved in this process, there are 28 possible arrows and thus more than 50 different parameters, Bialek said. Thus, creating a model of early fruit fly development with predictive power would require knowing what numbers to assign to all 50 or more parameters. Even in the well-studied case of fruit fly development, these numbers remain unknown. This is one very practical example in which even after one has carried out the reductionist work of identifying all of the constituent parts of a system, it is not necessarily possible to predict the behavior of that system as a whole from knowing the isolated behavior of its component parts.

Adding Systems-Level Ideas to the Reductionist Description

The variety of reactions to this problem of proliferation of parameters can be used, roughly, to classify the work being done in the field from different perspectives, including physics and systems biology, Bialek said. For instance, one approach is to concede that systems are so complicated that “quantitative biology” is really about learning complex models from limited data. Additional approaches, Bialek said, hold that (1) the only hope for a real theory is evolution (i.e., it is not about how things are, but about how they are related historically); (2) not all parameters matter; or (3) although there are many parameters at the micro scale, emergent functional phenomena are simpler. Bialek focused on an approach to the proliferation of parameters that involves adding systems-level ideas to the reductionist description. This approach presumes there is some principle that, in effect, selects the parameters, rather than parameter choices being random. The entire system has some function in the life of the organism, and the idea is to have a mathematical characterization of this function that makes it possible to optimize performance at this function, in parallel with what is being selected for by evolution. In the extreme, the hypothesis that function has been optimized by evolution can be considered, which would circumvent the need to know all of the parameters.

Candidate Principle: Transmit as Much Relevant Information as Possible with Limited Resources

Bialek described an example of a candidate principle that may operate at the system level: transmit as much relevant information as possible with limited resources. In the simplest case, X → Y (where X = input and Y = output), the question is how much information does the output provide about the input? For example, for every cell in an embryo to decide what body part it will become in the final pattern, it needs information about where it is located within the embryo. Each cell has an enormous amount of information and knows where it is to 1 percent accuracy, Bialek said. This level of precision is evident in cells’ positioning and the precision with which developmental events are reproducible between embryos. In the case of fruit flies, for instance, at just 3 hours into development there are fewer than 100 rows of cells along the length of the embryo, so that 1 percent precision means that every cell knows where it is, he said. A challenge in trying to “squeeze all of the information” out of these signaling molecules is that they are present at such low concentrations that any measurements of those concentrations will be noisy (variable due to a range of extrinsic or intrinsic factors). Squeezing out as much information as possible can be done in a mathematically precise way, Bialek said.

In considering how much information inputs and outputs provide about each other, it may seem as if the information cannot be more precise or accurate, particularly if the output is a noisy version of the input, Bialek said. However, that information does not depend exclusively on the noise level; it also depends on the distribution of signals moving through this input–output device. If the concentrations of the input molecules are always very low and the input-output device only turns on at a high concentration, then the device would always be off and no information would be transmitted, regardless of the noise level. Therefore, squeezing as much information through the system as possible depends on matching the input–output relationship, the noise level, and the distribution of inputs. These ideas date back to research done decades ago on vision, in which Laughlin argued that the input–output relationships of neurons in the fly retina were actually matched to the distribution of input light intensities that the insect encounters as it flies through the world (Laughlin, 1981). More generally, with fixed input/output relationship and noise, information can be maximized by adjusting the distribution of inputs (“achieving capacity”) or, with fixed noise and limited dynamic range at the output, information can be maximized by adjusting the mean input–output relation. This “matching” is a parameter-free prediction. In some cases, the neurons may require adaptation mechanisms that have not yet been identified but, more broadly,

the adaptation phenomena that have already been identified in the nervous system can be understood as accomplishing this kind of match.

Applying Parameter-Free Prediction to Genetic Regulatory Elements

Bialek returned to the early development of the fruit fly to explore the application of this type of parameter-free prediction to genetic regulatory elements. It is possible to conduct experiments to simultaneously measure the concentrations of one of the input molecules in every cell (i.e., the maternal signals) as well as the concentrations of one of the output or intermediate molecules (i.e., the gap genes), which reveals a sigmoidal relationship on average (Gregor et al., 2007). Because this work involves thousands of samples drawn from the relative probability distributions, it is possible to characterize the noise in the system in addition to the input–output relationship. Bialek discussed how to determine whether an input–output device that has this relationship between input concentration and output concentration—as well as this level of noise—transmits as much information as possible. Adjusting the distribution of input concentrations to push as much information through as possible—implementing the principle outlined above—becomes a numerical problem with no free parameters. This approach predicts the distribution of inputs but is more sensitive to the distribution of outputs, which is predicted to have a double-peaked form, but with some occupation of the intermediate levels, and this prediction is in good quantitative agreement with experiments (Tkačik et al., 2008). Bialek described this as one of the first indications that this vision of collecting information based on inputs and outputs made sense and that different aspects of the data are related to one another.

The next step along this path is to determine how to deal with more complex systems, which have multiple inputs and outputs, Bialek said. In the fly embryo, for example, the relevant information is not the morphogen concentration, but rather the position of cells in the embryo (Dubuis et al., 2013). Thus, tracing back to information about position yields more predictions about how the system should behave. Unfolding these ideas can make more explicit the algorithms needed to read out the information that is encoded in the various levels of expression. Including all the gap genes eliminates the ambiguities and recovers the 1 percent precision described above. This work can be tested using fruit fly genetics by observing mutants in which some maternal inputs have been deleted, Bialek added. Mutants defective in maternal inputs produce distorted patterns of gap gene expression. These algorithms can be used to read where a cell “thinks” it is in a mutant and then predict where pair-rule stripes should be, quantitatively and with no free parameters (Petkova et al., 2019).

Possible Advances Using Top-Down Principles

Injecting top-down, system-level principles can generate detailed, quantitative predictions, thus circumventing highly parameterized bottom-up models, Bialek said. However, a challenge with this approach is the inverse of the challenge raised by Anderson. That is, the most powerful experimental tools are microscopic: they are able to probe and manipulate biological systems at the molecular level, not the system level. It is clear that the bottom-up approach cannot be used all the way up to the system level. Moving forward with this approach, Bialek said, will require investigating whether these top-down principles can be used to reach all the way down to the molecular level.

APPLYING SYSTEMS THINKING TO THE DEVELOPMENT OF REGENERATIVE MEDICINES

In his presentation Zandstra provided two examples as a way to explore the application of systems thinking to the development of regenerative medicines in various contexts, ranging from translational problems to therapeutic applications.

Growing Blood Stem Cells as Therapies for Leukemia

Zandstra’s first example was centered on the work of growing blood stem cells as therapies for leukemia. This field was shaped by early discoveries and foundational observations published in the 1960s about how stem cells relate to their differentiated progeny and how a system—such as a distributed hematopoietic system—could be regulated through feedback control (Till et al., 1964). This example, Zandstra said, serves as a reminder that the foundation of systems biology and its use in regenerative medicine (i.e., stem cell biology) was established through observations and mathematical modeling conducted by physicists and hematologists who were seeking to understand cells. Specifically, Till and colleagues looked at how cells form colonies, investigated the properties of those colonies, and explored how components of the system interacted with one another to explain the responses of those colonies to transplantation and other processes. One of the early observations in this work was the potential role of feedback control in the cell creation system. This insight led to an investigation into why it is so difficult to grow blood stem cells when different cell types are generated that are continuously influencing their growth and differentiation. An empirical solution was developed by matching the rates of media addition and dilution of these cultures to the rates of secretion of inhibitory factors, which had a positive effect on the ex vivo expansion

of blood stem cells (Csaszar et al., 2012). However, Zandstra said, this approach did not provide an understanding of the complexity in the system represented by various molecules being secreted at varying rates either in static or “fed-batch” systems. Further work by Kirouac et al. (2010) elaborated on the structure and parametrization of the communication networks behind this feedback.

From Empirical to Mechanistic Modeling in Cell Therapy Process Development

Zandstra said that to move the field of cell therapy from empirical mechanistic modeling toward process development, the underlying molecular structures and mechanisms need to be integrated and considered as part of a larger model. This will require careful consideration about how those structures and mechanisms are integrated with the critical quality attributes (e.g., identity, purity, potency) and the measurements taken during these cultures¹ (Lipsitz et al., 2016). The intent, he said, is to move from completely empirical approaches to optimizing systems toward using more relevant data to define systems. In the context of a human stem cell–centric cell–cell communication network in which there are secreted factors in the system, this approach can be used to help elucidate which cells are secreting which factors, the directionality of these factors, and the overall function of the system when the factors are used to modulate the interaction networks. One example of research using an integrated systems approach involved the use of omics technologies to associate cell types within the hematopoietic system with certain molecules (Qiao et al., 2014). These molecules are associated with pathways, and those pathways are associated with effects, thus allowing for a reductionist representation of the cell communication network. Researchers then began to investigate those properties of the system that could be manipulated to change different aspects of the network (Caldwell et al., 2015). By rebalancing the network according to receptor expression, compartmentalization, and other methods of changing feedback via molecular components as well as overall niche components within the system, Zandstra and colleagues were able to generate next-generation bioreactors (Csaszar et al., 2014). These bioreactors can then be used to take baseline measurements of a cell culture system, measure key factors within the system, then control—in an automated fashion—the way media are added and the types of components that are added to the media. Using this approach has had a positive effect on the ability to grow total cells and

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¹ These measurements can include the gene expression signature of input cells, the fraction of proliferative T cell subtypes, cytokine activity, metabolite biomarker levels, and the pH rate of change.

progenitor cells, he added. Zandstra’s team has since implemented structures that underpin some of these bioreactor systems within clinical production processes for expanding blood stem cells. At the time of the workshop, more than 50 patients had been treated with expansion systems based, in part, on this fed-batch-based approach² (Cohen et al., 2020).

Generating Immunotherapies from Pluripotent Stem Cells

Zandstra used his second example, the generation of immunotherapies from pluripotent stem cells, to highlight a challenge in this field. The aim of the stem cell–derived manufacturing of immunotherapies is to move toward a universal, homogenous, and scalable off-the-shelf product. This is a challenging endeavor, Zandstra said, because generating mature T cells from stem cells involves a long and complex differentiation process: from pluripotent stem cells, either in their normal or engineered state, to blood progenitor cells, to progenitor T cells, and eventually to more mature T cells. One approach to this process is to develop technologies to control these various phases, which entails high degrees of complexity in terms of the timing, dosing, and types of molecules that are applied during the differentiation process. These factors likely control which types of progeny are produced from the progenitor T cells, including effector, regulatory, and other types of T cells in the system.

Computational Systems Modeling for the Predictive Design of T Cell Therapies

Zandstra explained that two signaling pathways are especially important in the process that differentiates pluripotent stem cells into various types of mature T cells: (1) Notch activation, which is necessary early on but must decrease as the cell moves toward T cell maturation, and (2) T cell receptor (TCR)-based signaling, which is eventually important for the proliferation and maturation of T cells. A major question is how to design environments that can control systems that involve such complex and multi-step processes (e.g., by quantitatively modulating Notch and TCR signaling to match in vivo thymopoiesis [the process by which thymocytes, a type of immune cell present in the thymus, are transformed into mature T cells]). Zandstra and his colleagues are working in this area at three different levels:

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² Fed-batch processes are partly open systems that involve intermittent or continuous feeding of nutrients. This approach can result in higher cell growth and product formation (Lim and Shin, 2013).

1. Mass action kinetics-based modeling of Notch-DLL4 signaling to explore how to quantitatively control biochemical pathways driving T cell fate;
2. Cell population modeling of thymopoiesis to understand how culture parameters modulate cell T cell differentiation and kinetics; and
3. Cellular kinetic pharmacokinetic/pharmacodynamic modeling to investigate how culture-generated T cell populations interact with human (patho-)physiology.

The first of these approaches seeks to achieve a basic understanding of the mass-action kinetics behind the signaling pathways that are activated by identifying the key signaling moieties that can be measured during the process. The second approach is related to cell population modeling and is similar to work within the hematopoietic system. This approach attempts to understand what factors—whether known or yet to be discovered from omics data—can be applied to guide the differentiation process. The third approach focuses on relating the key properties of cells measured in vitro to the overall biology of those cells in vivo, ideally in the patient. The systems pharmacology aspects of cell therapy products are still poorly understood, Zandstra added.

Zandstra went on to describe how Notch- and TCR-signaling models can be used for in silico bead design and optimization in order to look at the relationship between various signaling activation complexes on the surface of a progenitor cell and techniques that affect cell differentiation. In this endeavor the goal is to determine how signaling parameters affect cell differentiation. He noted that it is important to match the needs of the differentiation system with the signaling timing and processes that are under way.

Zandstra also presented a second example of how cellular kinetic pharmacokinetic/pharmacodynamic modeling can be used to understand the cellular properties underlying clinical response. As indicated by data on the signal of the chimeric antigen receptor (CAR) T cells in patients as a function of different patient examples, a major challenge is that clinical CAR T cell pharmacokinetic and exposure-response relationships are highly variable (Mueller et al., 2018). As a result, it has been difficult to understand what properties of cells should be measured to make predictions about the persistence of CAR T cells and their effects on tumors. By applying more complex models to processes that have developmental programs involving various T cell populations (e.g., naïve-memory T cells, effector T cells), it is possible to begin to simulate and extract from these models the parameters that may have the greatest ability to predict tumor mass reduction. As more data become available, the model’s ability to make relevant

predictions can be improved; this will feed back into informing the quality attributes around which cell cultures are designed and the ideal profiles of the cell therapy.

Applying Engineering Design Principles to Overcome Barriers in Cell Therapy Translation

There are opportunities to move the field forward by applying engineering design principles to overcome barriers in cell therapy translation, said Zandstra (Tewary et al., 2018). In the future, he said, it would be helpful to consider the point at which the systems component of mathematical modeling begins to extend beyond simple empirical models to more complex mechanistic models and, ultimately, to the types of emergent models discussed by Bialek. In such emergent models, the degree of complexity is so great that strategies are needed to extract key governing principles from those datasets. These techniques can be applied to understand, predict, and, eventually, control the cycle that underlies both discovery and translation, Zandstra added. Furthermore, these approaches could be applied to deal with some of the barriers faced in the field of regenerative medicine: for example, multi-scale aspects of systems, dynamics, heterogeneity, and the nonlinearity that is typically due to feedback control and other interactions within the models. Addressing those barriers, he said, has the potential to substantially improve the types of products that are produced for patients.

SYSTEMS DYNAMICS OF CELL-STATE TRANSITIONS: RELEVANCE FOR REGENERATIVE MEDICINE

Huang presented an exploration of systems dynamics of cell-state transitions and their relevance for regenerative medicine, with a focus on single-cell transcriptomics.

Cell Type Reprogramming as Cell-State Transition

Cell type reprogramming is a core process of interest throughout the field of regenerative medicine, Huang said. Researchers often seek to reprogram cells from one type to another through some form of manipulation; for example, transitioning induced pluripotent stem (iPS) cells into a particular type of neuron or transitioning pancreas α cells into pancreas β cells, which are useful for diabetes treatment. However, this vision is currently not fully aligned with reality, he said. In attempting to manipulate the cells in multicellular organisms with the intention of creating a desired cell type, a cell may be subjected to some intervention that can instead result in a variety of undesired cells. This is a problem for regenerative

medicine: not just the low rate of cells that respond (“failure to push hard enough”), but also the generation of many different cell types (“failure to channel”) is at the heart of the notorious inefficiency of any reprogramming manipulation. A systems perspective is needed in order to understand why this diversification happens, which cell types will be generated, and how to “herd” all the cells into the desired direction, he said.

Huang elaborated on the problem with the traditional, reductionist understanding of the process of cell type reprogramming as “molecular causation,” which is evident in models that consider a certain protein to cause a certain effect or phenotype. Using such causative pathway models, researchers try to block or stimulate proteins in order to prevent or promote the effect. This type of linear, molecular causation-based thinking is common across the biological sciences, he said, but it is not the appropriate perspective with which to approach this problem. From a stricter, formal standpoint it is more appropriate to consider the process in terms of a state transition, whereby some state (Cell Type 1) changes (i.e., transitions) to another state (Cell Type 2). For instance, through the process of state transition, a stem cell may become a differentiated cell, or a fibroblast may become an iPS cell. Within this perspective, the manipulation is intended to trigger the cell-state transition. This requires defining the state of the cell, which is governed by the gene regulatory network which has evolved to generate cell states and cell types.

Within the genome, every gene has some level of expression based on its profile, but the individual genes in the network are interdependent rather than independent with respect to altering their expression, Huang said. Changing the state of a cell changes the gene expression profile, but how individual genes contribute to this collective change is dictated by the network. The interactions within the network cannot be changed. Ultimately, what changes is not the network, but the state of the network with respect to the expression level of the individual genes that it contains. The network is hard-wired, but it changes its state as defined by the profile of the expression level of the genes. Since the genes are interdependent, some gene expression profiles are more likely to be realized (more stable) than others. Therefore, Huang explained, all possible gene expression profiles can be mapped to a sort of “potential landscape” in which the “elevation” crudely represent the probability of a given gene expression profile being realized. The potential wells (valleys) are the attractor states, which are the stable, observable gene expression profiles that fully satisfy the gene interaction rules imposed by the network (Chang et al., 2008; Huang et al., 2005; Zhou et al., 2012). The complex gene network of a genome generates multiple attractor states, a phenomenon called multi-stability. Each attractor is a cell type. Huang likened the study of transitions between attractor states to Waddington’s study of the epigenetic landscapes (Waddington, 1957).

Waddington attempted to frame development as a process that takes place on a landscape where the network seeks natural states (the valleys). This metaphor explains developmental robustness, discreteness of cell types, and instabilities that impose cell fate decisions, which are represented by the watersheds. Huang suggested that it would be valuable to apply this basic conceptual idea to regenerative medicine.

Complications to the Model of Cell-State Transitions

Huang described two complications to cell-state transitions within multicellular organisms with populations of millions of cells. Because of stochastic fluctuations, or non-genetic heterogeneity, these cells are all slightly different—even within a clonal cell population. Single-cell transcriptomics allows for a precise view of individual cells, while big data and statistical data analysis allow for individual cells to be plotted in a reduced dimensional space, creating clusters of various cells in various states. However, these individuated clusters, or subpopulations of cells, must be related to a theory that explains how a finite number of allowed attractor states can emerge from the gene regulatory network. Huang discussed novel advances in single-cell transcriptomes that are helping to advance this work. Traditionally, gene expression profiles are created by taking the entire population of millions of cells as one sample (e.g., by triggering differentiation and measuring gene expression across the entire cell culture), thus using population averages to study transcriptomes. However, by using single-cell-resolution measurements, a matrix can be generated in which each column is a cell, and each row is a gene. Single-cell resolution analysis can be used to perturb differentiation that changes the cell population structure, allowing changes in the cell–gene matrix to be observed instead of using an aggregate measure of the gene expression profile.

Another complication arises due to continued branching into various cell types, which may either be desired or undesired cell types. In the linear conception of such a process, a cell begins at some state, and a signal or intervention results in the change to a desired state. However, in a nonlinear process an intervention or signal may result in various and often polar-opposite states. Because cell-state changes are nonlinear, it is necessary to consider, beyond mere linear causation, the stability/instability/multi-stability of cell states. In addition, Huang said, the heterogeneity or stochasticity arising from each cell being in a slightly different state must be considered because those different cell states result in instability. To illustrate, Huang presented an animated model demonstrating the processes associated with cell-state changes. In order to transition between attractor states, the state space must be destabilized, which leads to a critical transition point at which the cell’s attractor state is flattened. With this destabilization comes

an element of uncontrollability. During the transitional cell states, some cells will move to the desired direction of the cell-state space, but others will move in aberrant directions toward an undesired outcome. This dispersion is reflected in single-cell analysis. The positions of individual cells in such analyses are governed by the underlying landscape which represents the constraints from the gene regulatory network. Stable clusters in these analyses represent the manifestation of the constraints of more and less stable states (i.e., the shape of the single-cell clusters and their changes reflect the dynamics on the epigenetic landscape).

Regarding the spontaneous branching of cell states, Huang said that after the cell state is destabilized, the cells disperse and hence become more different, which is readily measurable by single-cell gene expression analysis: the destabilization reduces the correlation between those cells. While this loss of correlation between the cells is intuitive to researchers in the field, what is more interesting is that in the same single-cell expression data matrix, the genes start to correlate with each other, Huang said. In summary, single-cell resolution measurement exposes destabilization and can be used to predict an impending bifurcation or “tipping point,” Huang said. At the transition, when maximally destabilized, just before the tipping point, the correlation between cell states will decrease while the correlation between genes will increase. By contrast, in the attractor state cells are maximally correlated (because they are forced to be in essentially the same state) while genes are uncorrelated (because the sole source of departure from the “set-point” expression level of a gene for each cell, imposed by the attractor state, is gene expression noise) (Mojtahedi et al., 2016).

Huang presented an example in which researchers attempted to differentiate iPS cells into cardiomyocytes (Trachana et al., 2018). In order to do this, it is necessary to transition cells along a particular path. As mentioned earlier, the practical challenge is overcoming the inefficiency of achieving directed differentiation, because some cells are lost to the wrong fate (Palpant et al., 2015). In this case, cells undergo two critical state transitions in the move from epiblast to primitive streak state, and they can arrive at various states that may or may not be desirable (Bargaje et al., 2017). Measuring cell–cell correlation reveals that in the move to the first jump, the cell–cell correlation decreases. However, in the same process, increasing numbers of gene-pairs suddenly start to correlate, suggesting a critical transition. The specific genes that correlate are important in this transition, as predicted by the theory: they are the ones that in the gene regulatory circuit regulate each other (hence correlate or anti-correlate with each other) and therefore likely are the genes that play central roles in driving the transition. However, there are also undesired cells that appear, which in this case are the endodermal lineages as opposed to the mesodermal lineages that lead to

the cardiomyocytes. This is the reason why reprogramming into a desired cell type is so inefficient, Huang said.

Huang emphasized that, in terms of systems thinking, the gene regulatory network that governs a gene expression profile as well as the quasi-potential (i.e., “epigenetic”) landscape and critical transitions (i.e., bifurcation) are important factors. The theory of such landscapes—and the measurements of cell–cell and gene–gene correlation explained previously—describes how individual states are more or less stable (relatively), especially with many cell types in a single population. Typical flow cytometry initially depicts just one dimension of the high-dimensional dynamics involved in cell transitions; however, single-cell data can elucidate high-dimensional dynamic states.

DISCUSSION

Expanding Beyond Empirical Modeling

Referring to an earlier remark by Zandstra that the systems component of mathematical modeling is becoming more than the mere application of empirical models, Zylberberg asked about the point at which the complexity becomes so great that key principles need to be extracted from datasets. This question is still being explored, Zandstra said, as researchers work to discover how to extract measurable parameters from global observations of cell states. The parameters may not be the identity of a molecule, but rather some combination of factors, including molecule, time, and perhaps some measure of concentration level. Together, a set of parameters could provide more information about a system than any individual measurement of a molecular state. While this is still a challenging area of study, there is progress being made toward understanding how a combination of parameters may offer insight into how those factors can influence different outcomes within culture systems, Zandstra said.

Noise in Biological Systems

Noise is important to consider because it can present an important challenge in understanding biological systems, Bialek said. He offered the analogy of an amplifier and speaker to demonstrate the concerns related to noise in a system. The output of an amplifier can be very noisy, despite the amplifier itself being nearly noiseless. In such a case, the noise may be created by a high-gain input that is being amplified. In the biological context, if concentrations of molecules are low, then all of the processes will be noisy—this is a feature of the physics or physical chemistry of the cell. What is unique in biological processes is that, for some reason, cells’ fates

are entrusted to a small number of molecules. This is a surprise, Bialek said, and operating in this regime makes the cells’ jobs difficult. Perhaps, he continued, much of what happens in the cell is shaped by the evolutionary choice to operate in this regime where noise plays such an important role. The presence of noise in the system does not reflect intrinsic sloppiness, he added.

In translational research and regenerative medicine development, it is sometimes difficult to distinguish between noise and a poorly specified system, Zandstra said. This can result in a poor understanding of key system parameters or an inappropriate technological design that is ill-matched to the current level of understanding. He offered an example from the early research on pluripotent stem cells: the cells would be put in an undefined aggregate (an embryoid body), and the variability in the types of differentiation that emerged were considered to be partially due to system noise. It has since been discovered that the introduction of high concentrations of inductive molecules at certain stages will lead to more uniform and coordinated differentiation. This is not to say that noise is not a part of the underlying biological process of the cell fate divisions, Zandstra said. Rather, it means that systems can be designed to control the impact of the noise.

Obtaining Rates for T Cell Phenotypes in the Transit Model

With regard to how rates are obtained for the different T cell phenotypes in the transit model, many data are gathered from the baseline process in which genomic, single-cell, and cell-level information is collected, Zandstra said. There are hundreds—if not thousands—of parameters that could be measured within complex systems, but data cannot reasonably be collected for every potential parameter. The use of more abstract models has helped to determine where parameter sensitivity has the greatest impact. It is helpful to strike a balance between measuring parameters that are aligned with existing outputs and searching for instances in which they are not aligned, Zandstra added.

Similarities to Quality-by-Design

Some of the concepts discussed during the session, namely those related to controlling processes in order to reach a desired endpoint, sound similar to quality-by-design approaches used in the chemical medicine space, a workshop participant pointed out. The data presented by Bialek and Huang can be thought of as a cloud of information that falls in the design space of quality-by-design, Zandstra said. This makes it possible to consider how to map process parameters to that cloud. It also provides the flexibility to determine which cells are in the cloud and thus how parameter and process

changes can be adapted while maintaining the desired attributes in cells. He suggested that this could provide a valuable opportunity to iterate faster around product development.

Choosing Targets Within Cell Systems

Addressing the issue of which attractor states are best for clinical efficacy in patients, Huang drew a distinction within the question between how researchers know which attractor cell to target (i.e., what kind of cell type is desired) and how these targets are realized. Referring to an example from his presentation, he described a situation where cardiomyocytes are desired but, in reality, a mixture of cell types would be needed due to the highly dynamic nature of cells. For example, in tumor therapy, in most cases one cannot simply kill tumor cells; it is necessary to account for other dynamics of tissues and tumors. Many cell types interact with other cell types, which presents a challenge for researchers. They must choose not only which attractor state to target, but also the distribution of millions of cells among different attractors that is necessary for cells to communicate with each other. If some cell-organizing principle were discovered in the future, it could make it possible to circumvent the need to understand every detail; instead it would be possible to simply trigger a process to keep development on the right path.

The history of models in developmental biology, Bialek said, began with Turing’s focus on how cells communicate and on the patterns emerging from those spatial interactions (Turing, 1952). The problem posed by Turing was how to make patterns form in the absence of any initial spatial inhomogeneities, but it was later appreciated that real embryos have “built in” spatial inhomogeneities. For example, a maternal effect gene at a particular place can drive every cell to make decisions, because it experiences a different concentration of the primary morphogen molecule. Consequently, the field bifurcated into one view that was dominated by a focus on interactions and another view that focused on cell autonomy. This bifurcation persists, in part, due to the nature of scientific experimentation. Disaggregating cells in order to study them individually makes it difficult to probe how they interact among each other. However, when cells are studied in aggregate, it is difficult to interrogate them individually—although there are now newer methods for studying cells together. Bialek suggested that once precision tools are available for interrogating individual cells in situ where their reactions can be probed, the two views may converge once again and demonstrate that the actual process contains elements of both conceptualizations. Discovering which organizing principles exist would be invaluable in revealing how those elements interact, he added.

Zandstra questioned how a network balancing within individual cells and the network structure may affect multi-scale tissue patterning. He and his colleagues recently made an initial effort to explore this issue at a simplistic level by looking at how rewiring in different levels of factors affects the Turing-like pattern events which occur in the simplest tissues.

Using Theory to Collect Data

Theory may be used not only to interpret data, but also to help reveal what types of data are most valuable to collect in order to build predictive models for cell-state conditions applied to cell therapies. Bialek commented that experimentation has a cyclical nature: some experiments spur theoretical insights that in turn raise new questions that can be investigated experimentally. The most interesting theoretical directions can depend on things that have not yet been measured, which drives researchers to return and make new measurements, Bialek said. For example, measuring the molecules in fly embryos at high precision is difficult, which discourages researchers from making such measurements unless they have some motivation or reason to think that a measurement at that level of precision would yield an interesting result. The question of how accurate a measurement needs to be is a theoretical one, Bialek said, because researchers are not generally inclined to collect measurements with greater precision than necessary just for the sake of doing so. While some questions are obvious to researchers even without a theory to motivate them, many of the details of experimental design—such as how many things need to be measured simultaneously, measurement accuracy, and the time resolution required to resolve transitions—are (or should be) informed by theory.

Theory plays a role in determining how precise measurements should be, Zylberberg added. Theory is at times purely academic, Huang said, noting that individuals may have unrealistic expectations for what theory can do. Theory offers a broad view, and it is generally beneficial for researchers to understand theory and then decide to what extent it will guide analysis. Currently, there is too much reliance on purely computational approaches, Huang said, but theory could be helpful to counteract this reliance, especially to the extent that it may reveal instances where it is not necessary to collect the fullest possible detail in terms of measurement.

Much of the session’s discussion of systems had been related to cell engineering and decision making at the level of individual cells, Zylberberg noted. She posed a question to the panelists from an audience member about how the boundaries of a system are determined and asked whether there have been instances where the system had to be narrowed or broadened. System boundaries are drawn based on an inference that those

boundaries will be productive, Bialek said, not on a belief that a system’s interactions do not cross those boundaries. In the history of biology, Bialek said, progress has often been related to the degree to which processes being studied have been able to be isolated. For instance, in neuroscience that which is well understood is primarily related to situations in which one thing happens in one place. The less isolated that processes are, the more difficult it is to understand those processes. The drawing of boundaries is always considered, and such boundary drawing should be acknowledged as a component of the hypothesis itself. However, Bialek said, because boundaries are selected with the intent of making progress within those boundaries, one mode of failure may be the recognition that processes cross the boundaries too often for progress to be made within them. There is an iterative aspect to this process that is characteristic of all work on biological systems, he said. In some cases, such as in studying single molecules, the elements being studied are removed from their complex context in order to ensure that nothing goes in or out. In some ways this is productive, Bialek said, but in other ways it can sacrifice potentially important observations. Huang said that there is sometimes a dismissive attitude toward any work that is decontextualized. However, he pointed out that science must work through dissection. For instance, the heart could only be studied because scientists removed a heart from a dead body. This can be done operationally while still being aware of context, he noted.

Each type of entropy—Shannon, Tsallis, and Renyi—has its uses for capturing information,³ Bialek said, but Shannon entropy corresponds to intuitions about what information means and is the same as the entropies familiar from physical chemistry, statistical mechanics, and other fields. Other entropies have value as well, in part because they are easier to estimate from finite data, making possible a broader range of connections between theory and experiment. However, on a conceptual basis, he said, Shannon entropy is privileged.

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³ For an overview of these different entropies, see Amigo et al. (2018).